Finite Group Databasebeta

← #19144576

Subgroups — #19144576

Order 5504.

398 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583479C211yesmaximal, characteristic
2#14583379C211yesmaximal, characteristic, complemented
3#14583239C211yesmaximal, characteristic, complemented
4#14583233C211yesmaximal, characteristic, complemented
5#14583232C211yesmaximal, characteristic, complemented
6#14583225C211yesmaximal, characteristic, complemented
7#14583223C211yesmaximal, characteristic, complemented
8#14583214C211yesmaximal, characteristic, complemented
9#14583213C211yesmaximal, characteristic, complemented
10#14582938C211yesmaximal, characteristic, complemented
11#107×D43C211yesmaximal, characteristic, complemented
12#14582899C211yesmaximal, characteristic, complemented
13#14582894C211yesmaximal, characteristic, complemented
14#14582864C211yesmaximal, characteristic, complemented
15C43×#485C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621898C2211yescharacteristic
18C2×#10621872C2211yescharacteristic
19C2×C8×D43C2211yescharacteristic
20#13063303—21no—
21#13063301C2211yescharacteristic
22#13063300—21no—
23#13063300C2211yescharacteristic
24#13063299C2211yescharacteristic
25#13063298—21no—
26#13063298—21no—
27C4×Dic86—21no—
28C4×D172—21no—
29(C22⋊D43)⋊C4—21no—
30(C22⋊D43)⋊C4—21no—
31#13063283C2211yescharacteristic
32#13063283C2211yescharacteristic
33C2×C4⋊Dic43C2211yescharacteristic
34C4⋊C4×D43C2211yescharacteristic
35C4⋊C4×D43C2211yescharacteristic
36C4⋊C4×D43C2211yescharacteristic
37#13063259C2211yescharacteristic
38#13063259C2211yescharacteristic
39#13063258C2211yescharacteristic
40#13063258C2211yescharacteristic
41#13063258C2211yescharacteristic
42#13063256C2211yescharacteristic
43#13063249C2211yescharacteristic
44#13063249C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51(C2×D43)⋊C8C2211yescharacteristic
52C22⋊Q8×C43C2211yescharacteristic
53#117×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#106×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C22×C4×C43C2311yescharacteristic
61C2×C22⋊D43—21no—
62C2×C22⋊D43D411yescharacteristic
63C2×C22⋊D43D411yescharacteristic
64C22×Dic43—21no—
65#10621902—22no—
66#10621902—22no—
67#10621898—22no—
68#10621898—22no—
69C2×D172—21no—
70C2×D172—21no—
71C2×D172D411yescharacteristic
72C2×D172C2311yescharacteristic
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43C2311yescharacteristic
78C2×C4×D43C2311yescharacteristic
79C2×Dic86D411yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C2×C8×C43C2311yescharacteristic
82C4⋊C4×C43—21no—
83C4⋊C4×C43C2311yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C4⋊C4×C43C2311yescharacteristic
86C22⋊C4×C43—21no—
87C22⋊C4×C43—21no—
88C42×C43—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94C4⋊Dic43—21no—
95C4⋊Dic43C2311yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97C4⋊Dic43C2311yescharacteristic
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106#10621872—22no—
107C8×D43—22no—
108C23×C43C2×D411yescharacteristic
109C22×D43—21no—
110C22×D43C2×D411yescharacteristic
111C22×D43C2×D411yescharacteristic
112Q8×C43—21no—
113Q8×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43C2×D411yescharacteristic
121C2×C4×C43C2411yescharacteristic
122C22⋊D43—22no—
123C22⋊D43—22no—
124C22⋊D43—81no—
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43—81no—
129C2×Dic43C2×D411yescharacteristic
130C2×Dic43C2×D411yescharacteristic
131D172—22no—
132D172—21no—
133D172—21no—
134D172—42no—
135D172—81no—
136C4×D43—21no—
137C4×D43—21no—
138C4×D43—42no—
139C4×D43—81no—
140C4×D43—81no—
141C4×D43—81no—
142C4×D43#4112yes—
143C4×D43#4112yes—
144Dic86—22no—
145C8×C43—21no—
146C8×C43—21no—
147C43⋊C8—21no—
148C43⋊C8—21no—
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—21no—
152C22×C43C22×D411yescharacteristic
153C2×D43—21no—
154C2×D43—21no—
155C2×D43—21no—
156C2×D43—21no—
157C2×D43—21no—
158C2×D43—41no—
159C2×D43—41no—
160C2×D43—41no—
161C2×D43#12312yes—
162C4×C43—21no—
163C4×C43—41no—
164C4×C43—41no—
165C4×C43—41no—
166C4×C43—41no—
167C4×C43C2×#4111yescharacteristic
168C4×C43C2×#4111yescharacteristic
169Dic43—21no—
170Dic43—41no—
171Dic43—41no—
172Dic43—41no—
173Dic43#12312yes—
174#3098—431nomaximal, Sylow
175C2×C43—41no—
176C2×C43C2×#12311yescharacteristic
177C2×C43#57611yescharacteristic
178C2×C43#57811yescharacteristic
179D43—22no—
180D43—41no—
181D43—81no—
182#537—431no—
183#520—431no—
184#485—431no—
185#485D4311yescharacteristic, complemented
186#484—431no—
187#484—431no—
188#482—431no—
189#482—431no—
190#480—431no—
191#480—431no—
192#428—431no—
193C2×#107—431no—
194#417—431no—
195#416—431no—
196#408—431no—
197C43#309811yescharacteristic, complemented, Sylow
198C2×#41—431no—
199C2×#41—431no—
200C2×M16—431no—
201C22×C8—431no—
202C22⋊Q8—431no—
203C22⋊Q8—861no—
204C22⋊Q8C2×D4311yescharacteristic
205#121—431no—
206#121—431no—
207#121—861no—
208#121—861no—
209#121—861no—
210C4×Q8—861no—
211C4×D4—861no—
212C4×D4—861no—
213C4×D4—861no—
214#117—431no—
215#117—431no—
216#117C2×D4311yescharacteristic
217C2×C4⋊C4—431no—
218C2×C4⋊C4—431no—
219C2×C4⋊C4—431no—
220C2×C4⋊C4—431no—
221#107—431no—
222#107—431no—
223#107—431no—
224#107—431no—
225#107—431no—
226#107C2×D4311yescharacteristic
227#106—431no—
228#106C2×D4311yescharacteristic
229#103—431no—
230#103—431no—
231#103C2×D4311yescharacteristic
232#103C2×D4311yescharacteristic
233#102—431no—
234#102—431no—
235#102—431no—
236#102—431no—
237C22⋊C8—431no—
238C22⋊C8—431no—
239C22⋊C8—431no—
240C22⋊C8C2×D4311yescharacteristic
241#41—862no—
242#41—862no—
243#41—862no—
244#41—862no—
245C2×Q8—431no—
246C2×Q8C22×D4311yescharacteristic
247C2×D4—431no—
248C2×D4—431no—
249C2×D4—431no—
250C2×D4—431no—
251C2×D4—861no—
252C2×D4—861no—
253C2×D4—861no—
254C22×C4—431no—
255C22×C4—431no—
256C22×C4—861no—
257C22×C4—861no—
258C22×C4—861no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4C22×D4311yescharacteristic
262M16—862no—
263C2×C8—431no—
264C2×C8—431no—
265C2×C8—862no—
266C2×C8C22×D4311yescharacteristic
267C2×C8C22×D4311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—431no—
270C4⋊C4—431no—
271C4⋊C4—431no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4—861no—
275C4⋊C4—861no—
276C4⋊C4—861no—
277C4⋊C4C22×D4311yescharacteristic
278C4⋊C4C22×D4311yescharacteristic
279C4⋊C4C22×D4311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C22⋊C4—861no—
287C42—21no—
288C42—861no—
289C42—861no—
290C23—431no—
291C23—431no—
292C23—861no—
293C23D4×D4311yescharacteristic
294Q8—21no—
295Q8—21no—
296Q8—862no—
297D4—862no—
298D4—862no—
299D4—862no—
300D4—861no—
301D4—861no—
302D4—3441no—
303D4—3441no—
304D4—1722no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—431no—
312C2×C4—432no—
313C2×C4—432no—
314C2×C4—431no—
315C2×C4—861no—
316C2×C4—861no—
317C2×C4—861no—
318C2×C4—861no—
319C2×C4—861no—
320C2×C4—3441no—
321C2×C4—3441no—
322C2×C4—3441no—
323C2×C4—3441no—
324C2×C4—1722no—
325C2×C4D4×D4311yescharacteristic
326C2×C4C23×D4311yescharacteristic
327C8—21no—
328C8—21no—
329C8—861no—
330C8—861no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—432no—
335C22—861no—
336C22—861no—
337C22—861no—
338C22—861no—
339C22—861no—
340C22—1721no—
341C22—1721no—
342C22—1721no—
343C22C2×D4×D4311yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—432no—
350C4—861no—
351C4—1721no—
352C4—1721no—
353C4—1721no—
354C4#41×D4311yescharacteristic
355C4#41×D4311yescharacteristic
356C2—41no—
357C2—862no—
358C2—3441no—
359C2—1721no—
360C2#123×D4311yescharacteristic
361C2#1458370111yescharacteristic
362C2#1458371511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#485C2
socleC22×C43C22×D4
hypercenter#485D43
hypocenterC43#3098
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #14583379C2semidirect
3. #14583239C2semidirect
4. #14583233C2semidirect
5. #14583232C2semidirect
6. #14583225C2semidirect
7. #14583223C2semidirect
8. #14583214C2semidirect
9. #14583213C2semidirect
10. #14582938C2semidirect
11. #107×D43C2semidirect
12. #14582899C2semidirect
13. #14582894C2semidirect
14. #14582864C2semidirect
15. C43×#485C2semidirect
185. #485D43semidirect
197. C43#3098semidirect